Recursive parameter identification of constrained systems: an application to electrically stimulated muscle

A method of incorporating constraints on model parameters is developed. This method is applicable to most recursive parameter-identification algorithms. It enforces linear equality constraints on identified parameters. The use of this method for the real-time identification of autoregressive-moving-average time series models, subject to parameter constraints, is described. These constraints may be time varying. The use of this algorithm is demonstrated in the identification of electrically stimulated quadriceps muscles in paraplegic human subjects, using percutaneous intramuscular electrodes. The nonlinear steady-state force versus pulsewidth recruitment characteristic of the electrode-muscle system is identified simultaneously with the input-output muscle response dynamics, using a Hammerstein-type model. Knowledge of the recruitment curve's shape is translated into constraints on the identified parameters. This information improves the experimental predictive quality of the identified model.